Exploratory Subgroup Identification with ForestSearch

German Breast Cancer Study Group (GBSG) Analysis

Author

Larry F. León

Published

February 9, 2026

1 Introduction

This vignette demonstrates the ForestSearch methodology for exploratory subgroup identification in survival analysis, as described in León et al. (2024) Statistics in Medicine.

1.1 Motivation

In clinical trials, particularly oncology, subgroup analyses are essential for:

Evaluating treatment effect consistency across patient populations
Identifying subgroups where treatment may be detrimental (harm)
Characterizing subgroups with enhanced benefit
Informing regulatory decisions and clinical practice

While prespecified subgroups provide stronger evidence, important subgroups based on patient characteristics may not be anticipated. ForestSearch provides a principled approach to exploratory subgroup identification with proper statistical inference.

1.2 Methodology Overview

ForestSearch identifies subgroups through:

Candidate factor selection: Using LASSO and/or Generalized Random Forests (GRF)
Exhaustive subgroup search: Evaluating all combinations up to maxk factors
Consistency-based selection: Applying splitting consistency criteria
Bootstrap bias correction: Adjusting for selection-induced optimism
Cross-validation: Assessing algorithm stability

The key innovation is the splitting consistency criterion: a subgroup is considered “consistent with harm” if, when randomly split 50/50 many times, both halves consistently show hazard ratios ≥ 1.0 (for example if 1.0 represents a meaningful “harm threshold”).

2 Setup

2.1 Load Required Packages

Show code

library(forestsearch)
library(survival)
library(data.table)
library(ggplot2)
library(gt)
library(grf)
library(policytree)
library(doFuture)
library(doRNG)

# Optional packages for enhanced output
library(patchwork)
library(weightedsurv)

# Set ggplot theme
theme_set(theme_minimal(base_size = 12))

3 Data: German Breast Cancer Study Group Trial

3.1 Study Background

The GBSG trial evaluated hormonal treatment (tamoxifen) versus chemotherapy in node-positive breast cancer patients. Key characteristics:

Sample size: N = 686
Outcome: Recurrence-free survival time
Censoring rate: ~56%
Treatment: Hormonal therapy (tamoxifen) vs. chemotherapy

3.2 Data Preparation

Show code

# Load GBSG data (included in forestsearch package)
df.analysis <- gbsg

# Prepare analysis variables
df.analysis <- within(df.analysis, {
  id <- seq_len(nrow(df.analysis))
  time_months <- rfstime / 30.4375
  grade3 <- ifelse(grade == "3", 1, 0)
  treat <- hormon
})

# Define variable roles
confounders.name <- c("age", "meno", "size", "grade3", "nodes", "pgr", "er")
outcome.name <- "time_months"
event.name <- "status"
id.name <- "id"
treat.name <- "hormon"

# Display data structure
cat("Sample size:", nrow(df.analysis), "\n")

Sample size: 686

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cat("Events:", sum(df.analysis[[event.name]]), 
    sprintf("(%.1f%%)\n", 100 * mean(df.analysis[[event.name]])))

Events: 299 (43.6%)

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cat("Baseline factors:", paste(confounders.name, collapse = ", "), "\n")

Baseline factors: age, meno, size, grade3, nodes, pgr, er

3.3 Baseline Characteristics

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create_summary_table(
  data = df.analysis,
  treat_var = treat.name,
  table_title = "GBSG Baseline Characteristics by Treatment Arm",
  vars_continuous = c("age", "nodes", "size", "er", "pgr"),
  vars_categorical = c("grade", "meno"),
  font_size = 12
)

Characteristic		Control (n=440)	Treatment (n=246)	P-value¹	SMD²
GBSG Baseline Characteristics by Treatment Arm
age	Mean (SD)	51.1 (10.0)	56.6 (9.4)	<0.001	0.57
nodes	Mean (SD)	4.9 (5.6)	5.1 (5.3)	0.665	0.03
size	Mean (SD)	29.6 (14.4)	28.8 (14.1)	0.470	0.06
er	Mean (SD)	79.7 (124.2)	125.8 (191.1)	<0.001	0.30
pgr	Mean (SD)	102.0 (170.0)	124.3 (249.7)	0.213	0.11
grade				0.273	0.06
	1	48 (10.9%)	33 (13.4%)
	2	281 (63.9%)	163 (66.3%)
	3	111 (25.2%)	50 (20.3%)
meno				<0.001	0.27
	0	231 (52.5%)	59 (24.0%)
	1	209 (47.5%)	187 (76.0%)
¹ P-values: t-test for continuous, chi-square/Fisher's exact for categorical/binary variables
² SMD = Standardized mean difference (Cohen's d for continuous, Cramer's V for categorical)

3.4 Kaplan-Meier Analysis (ITT Population)

Show code

# Prepare counting process data for KM plot
dfcount <- df_counting(
  df = df.analysis,
  by.risk = 6,
  tte.name = outcome.name,
  event.name = event.name,
  treat.name = treat.name
)

# Plot with confidence intervals and log-rank test
plot_weighted_km(
  dfcount,
  conf.int = TRUE,
  show.logrank = TRUE,
  ymax = 1.05,
  xmed.fraction = 0.775,
  ymed.offset = 0.125
)

The ITT Cox hazard ratio estimate is approximately 0.69 (95% CI: 0.54, 0.89), suggesting an overall benefit for hormonal therapy.

4 Preliminary Analysis: Generalized Random Forests

Before running ForestSearch, we can use GRF to explore potential treatment effect heterogeneity and identify candidate factors.

Show code

t0 <- proc.time()

grf_est <- grf.subg.harm.survival(
  data = df.analysis,
  confounders.name = confounders.name,
  outcome.name = outcome.name,
  event.name = event.name,
  id.name = id.name,
  treat.name = treat.name,
  maxdepth = 2,
  n.min = 60,
  dmin.grf = 12,
  frac.tau = 0.6,
  details = TRUE,
  return_selected_cuts_only = FALSE
)

tau, maxdepth = 46.75811 2 
   leaf.node control.mean control.size control.se depth
1          2         6.49        82.00       3.34     1
2          3        -4.10       604.00       1.06     1
11         4        -7.90       112.00       2.81     2
21         5         3.86       177.00       1.87     2
4          7        -5.89       356.00       1.33     2

Selected subgroup:
  leaf.node control.mean control.size control.se depth
1         2         6.49        82.00       3.34     1

GRF subgroup found
Terminating node at max.diff (sg.harm.id):
[1] "er <= 0"

All splits (from all trees):
[1] "er <= 0"   "age <= 50" "age <= 43"

Show code

timings$grf <- (proc.time() - t0)["elapsed"]

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# Display policy trees
# leaf1 = recommend control, leaf2 = recommend treatment
par(mfrow = c(1, 2))
plot(grf_est$tree1, leaf.labels = c("Control", "Treat"), main = "Depth 1")

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plot(grf_est$tree2, leaf.labels = c("Control", "Treat"), main = "Depth 2")

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par(mfrow = c(1, 1))

GRF identifies estrogen receptor status (ER) as a key factor, with ER ≤ 0 suggesting potential harm from hormonal therapy.

5 ForestSearch Analysis

5.1 Parallel Processing Configuration

ForestSearch supports parallel processing for computationally intensive operations (bootstrap, cross-validation).

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# Detect available cores (use fewer for CRAN checks)
n_cores <- min(parallel::detectCores() - 1, 20)
cat("Using", n_cores, "cores for parallel processing\n")

Using 13 cores for parallel processing

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# Configure parallel backend
registerDoFuture()
registerDoRNG()

5.2 Running ForestSearch

ForestSearch performs an exhaustive search over candidate subgroup combinations with up to maxk factors. Key parameters:

Parameter	Value	Description
`hr.threshold`	1.25	Minimum HR for consistency evaluation
`hr.consistency`	1.0	Minimum consistency rate for candidates
`pconsistency.threshold`	0.90	Required consistency for selection
`maxk`	2	Maximum factors in subgroup definition
`n.min`	60	Minimum subgroup sample size
`d0.min`, `d1.min`	12	Minimum events per treatment arm

Show code

t0 <- proc.time()

fs <- forestsearch(
  df.analysis,
  confounders.name = confounders.name,
  outcome.name = outcome.name,
  treat.name = treat.name,
  event.name = event.name,
  id.name = id.name,
  # Threshold parameters (per León et al. 2024)
  hr.threshold = 1.25,
  hr.consistency = 1.0,
  pconsistency.threshold = 0.90,
  stop_threshold = 0.95,
  # Search configuration
  sg_focus = "hrMaxSG",
  max_subgroups_search = 10,
  use_twostage = TRUE,
  # Factor selection
  use_grf = TRUE, 
  return_selected_cuts_only = TRUE,
  use_lasso = TRUE,
  cut_type = "default",
  # Subgroup constraints
  maxk = 2,
  n.min = 60,
  d0.min = 10,
  d1.min = 10,
  # Consistency evaluation
  fs.splits = 400,
  # Parallel processing
  parallel_args = list(
    plan = "multisession",
    workers = n_cores,
    show_message = TRUE
  ),
  # Output options
  showten_subgroups = TRUE,
  details = TRUE,
  plot.sg = TRUE
)

Note: stop_threshold reset to NULL for sg_focus = 'hrMaxSG'.
Early stopping disabled when HR is prioritized in selection;
Also consider increasing max_subgroups_search if search does not appear exhaustive.


=== Two-Stage Consistency Evaluation Enabled ===
Stage 1 screening splits: 30 
Maximum total splits: 400 
Batch size: 20 
================================================

GRF stage for cut selection with dmin, tau = 12 0.6 
  return_selected_cuts_only = TRUE: using cuts from selected tree only
tau, maxdepth = 46.75811 2 
   leaf.node control.mean control.size control.se depth
1          2         6.49        82.00       3.34     1
2          3        -4.10       604.00       1.06     1
11         4        -7.90       112.00       2.81     2
21         5         3.86       177.00       1.87     2
4          7        -5.89       356.00       1.33     2

Selected subgroup:
  leaf.node control.mean control.size control.se depth
1         2         6.49        82.00       3.34     1

GRF subgroup found
Terminating node at max.diff (sg.harm.id):
[1] "er <= 0"

Cuts from selected tree (depth = 1 ):
[1] "er <= 0"
GRF cuts identified: 1 
  Cuts: er <= 0 
  Selected tree depth: 1 
# of continuous/categorical characteristics 5 2 
Continuous characteristics: age size nodes pgr er 
Categorical characteristics: meno grade3 
## Prior to lasso: age size nodes pgr er 
#### Lasso selection results 
7 x 1 sparse Matrix of class "dgCMatrix"
                 s0
age     .          
meno    .          
size    0.005433435
grade3  0.178139021
nodes   0.049670523
pgr    -0.001812895
er      .          
Cox-LASSO selected: size grade3 nodes pgr 
Cox-LASSO not selected: age meno er 
### End Lasso selection 
## After lasso: size nodes pgr 
Default cuts included from Lasso: size <= mean(size) size <= median(size) size <= qlow(size) size <= qhigh(size) nodes <= mean(nodes) nodes <= median(nodes) nodes <= qlow(nodes) nodes <= qhigh(nodes) pgr <= mean(pgr) pgr <= median(pgr) pgr <= qlow(pgr) pgr <= qhigh(pgr) 
Categorical after Lasso: grade3 
Factors per GRF: er <= 0 
Initial GRF cuts included er <= 0 
Factors included per GRF (not in lasso) er <= 0 

===== CONSOLIDATED CUT EVALUATION (IMPROVED) =====
Evaluating 14 cut expressions once and caching...
Cut evaluation summary:
  Total cuts:  14 
  Valid cuts:  14 
  Errors:  0 
✓ All 14 factors validated as 0/1
===== END CONSOLIDATED CUT EVALUATION =====

# of candidate subgroup factors= 14 
 [1] "er <= 0"      "size <= 29.3" "size <= 25"   "size <= 20"   "size <= 35"  
 [6] "nodes <= 5"   "nodes <= 3"   "nodes <= 1"   "nodes <= 7"   "pgr <= 110"  
[11] "pgr <= 32.5"  "pgr <= 7"     "pgr <= 131.8" "grade3"      
Number of possible configurations (<= maxk): maxk = 2 , # combinations = 406 
Events criteria: control >= 10 , treatment >= 10 
Sample size criteria: n >= 60 
Subgroup search completed in 0.01 minutes

--- Filtering Summary ---
  Combinations evaluated: 406 
  Passed variance check: 374 
  Passed prevalence (>= 0.025 ): 374 
  Passed redundancy check: 354 
  Passed event counts (d0>= 10 , d1>= 10 ): 270 
  Passed sample size (n>= 60 ): 263 
  Cox model fit successfully: 263 
  Passed HR threshold (>= 1.25 ): 8 
-------------------------

Found 8 subgroup candidate(s)
# of candidate subgroups (meeting all criteria) = 8 
Random seed set to: 8316951 
Two-stage parameters:
  n.splits.screen: 30 
  screen.threshold: 0.763 
  batch.size: 20 
  conf.level: 0.95 
# of unique initial candidates: 8 
# Restricting to top stop_Kgroups = 10 
# of candidates to evaluate: 8 

================================================================================ 
TOP 8 CANDIDATE SUBGROUPS FOR CONSISTENCY EVALUATION
Sorted by: hrMaxSG 
================================================================================ 

Rank   HR        N       Events  K    Subgroup Definition
-------------------------------------------------------------------------------- 
1      2.537     61      34      2    {er <= 0} & {size <= 35}
2      2.335     61      31      2    {er <= 0} & {nodes <= 7}
3      2.222     75      41      2    {er <= 0} & {pgr <= 32.5}
4      2.054     61      35      2    {er <= 0} & !{size <= 20}
5      1.992     64      34      2    {er <= 0} & {pgr <= 7}
6      1.951     82      45      1    {er <= 0}
7      1.710     72      39      2    {grade3} & {pgr <= 7}
8      1.319     71      29      2    !{size <= 35} & {nodes <= 5}
--------------------------------------------------------------------------------

Parallel config: workers = 13 , batch_size = 8 
Batch 1 / 1 : candidates 1 - 8 
Evaluated 8 of 8 candidates (complete) 
6 subgroups passed consistency threshold

*** Subgroup found: {er <= 0} 
% consistency criteria met= 0.92 
SG focus = hrMaxSG 
Seconds and minutes forestsearch overall = 6.752 0.1125 
Consistency algorithm used: twostage

Show code

plan("sequential")
timings$forestsearch <- (proc.time() - t0)["elapsed"]

cat("\nForestSearch completed in", 
    round(timings$forestsearch, 1), "seconds\n")


ForestSearch completed in 6.8 seconds

5.3 ForestSearch Results

5.3.1 Identified Subgroups

Show code

# Generate results tables
res_tabs <- sg_tables(fs, ndecimals = 3, which_df = "est")

# Display top subgroups meeting criteria
res_tabs$sg10_out

Factor 1	Factor 2	N	Events	E₁	HR	P_cons
Identified Subgroups
Two-factor subgroups (maxk=2)
{er <= 0}		82	45	16	1.951	0.920
{er <= 0}	{pgr <= 32.5}	75	41	16	2.222	0.990
{er <= 0}	{pgr <= 7}	64	34	13	1.992	0.920
{er <= 0}	{size <= 35}	61	34	15	2.537	0.990
{er <= 0}	{nodes <= 7}	61	31	11	2.335	0.940
{er <= 0}	!{size <= 20}	61	35	12	2.054	0.940
Search Configuration: Single-factor candidates (L) = 28; Maximum combinations evaluated = 406; Search depth (maxk) = 2
Search Results: Candidate subgroups found = 8; Maximum HR estimate = 2.54
Note: E₁ = events in treatment arm; P_cons = consistency proportion

5.3.2 Treatment Effect Estimates

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# ITT and subgroup estimates
res_tabs$tab_estimates

Subgroup	n	n1	events	m1	m0	RMST	HR (95% CI)
Treatment Effect Estimates
Training data estimates
ITT	686 (100.0%)	246 (35.9%)	299 (43.6%)	66.3	50.2	7.8	0.69 (0.54, 0.89)
Questionable¹	82 (12.0%)	26 (31.7%)	45 (54.9%)	22.9	43.7	-14	1.95 (1.04, 3.67)
Recommend	604 (88.0%)	220 (36.4%)	254 (42.1%)	66.7	52.6	9.3	0.61 (0.47, 0.80)
¹ Identified subgroup : {er <= 0}

5.3.3 Identified Subgroup Definition

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cat("Identified subgroup (H):", paste(fs$sg.harm, collapse = " & "), "\n")

Identified subgroup (H): {er <= 0}

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cat("Subgroup size:", sum(fs$df.est$treat.recommend == 0), 
    sprintf("(%.1f%% of ITT)\n", 
            100 * mean(fs$df.est$treat.recommend == 0)))

Subgroup size: 82 (12.0% of ITT)

ForestSearch identifies Estrogen ≤ 0 (ER-negative) as the subgroup with potential harm. This is biologically plausible: tamoxifen is a selective estrogen receptor modulator with limited efficacy in ER-negative tumors.

6 Bootstrap Bias Correction

6.1 Rationale

Cox model estimates from identified subgroups are upwardly biased due to the selection process (subgroups are selected because they show extreme effects). Bootstrap bias correction addresses this by:

Resampling with replacement
Re-running the entire ForestSearch algorithm
Computing bias terms from bootstrap vs. observed estimates
Applying infinitesimal jackknife variance estimation

6.2 Running Bootstrap Analysis

Show code

# Number of bootstrap iterations
# Use 500-2000 for production; reduced here for vignette
NB <- 1000

t0 <- proc.time()

fs_bc <- forestsearch_bootstrap_dofuture(
  fs.est = fs,
  nb_boots = NB,
  show_three = FALSE,
  details = FALSE
)

plan("sequential")
timings$bootstrap <- (proc.time() - t0)["elapsed"]

cat("\nBootstrap completed in", 
    round(timings$bootstrap / 60, 1), "minutes\n")


Bootstrap completed in 9.3 minutes

6.3 Bootstrap Summary and Diagnostics

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# Comprehensive summary with diagnostics
summaries <- summarize_bootstrap_results(
  sgharm = fs$sg.harm,
  boot_results = fs_bc,
  create_plots = TRUE,
  est.scale = "hr"
)


===============================================================
           BOOTSTRAP ANALYSIS SUMMARY                          
===============================================================

IDENTIFIED SUBGROUP:
-------------------------------------------------------------
  H: {er <= 0}

BOOTSTRAP SUCCESS METRICS:
-------------------------------------------------------------
  Total iterations:              1000
  Successful subgroup ID:        874 (87.4%)
  Failed to find subgroup:       126 (12.6%)

TIMING ANALYSIS:
-------------------------------------------------------------
Overall:
  Total bootstrap time:          9.28 minutes (0.15 hours)
  Average per iteration:         0.01 min (0.6 sec)

Show code

# Display bias-corrected estimates table
summaries$table

Subgroup	Sample Size			Survival			Treatment Effect
Treatment Effect by Subgroup
Bootstrap bias-corrected estimates (1000 iterations)
Subgroup	N	N_T	Events	Med_T	Med_C	RMST_d	HR (95% CI)^†¹	HR^‡ (95% CI)²
Qstnbl³	82 (12.0%)	26 (31.7%)	45 (54.9%)	22.9	43.7	-14	1.95 (1.04, 3.67)	1.53 (0.8,2.93)
Recmnd	604 (88.0%)	220 (36.4%)	254 (42.1%)	66.7	52.6	9.3	0.61 (0.47, 0.80)	0.64 (0.44,0.93)
¹ Unadjusted HR: Standard Cox regression hazard ratio with robust standard errors
² Bias-corrected HR: Bootstrap-adjusted estimate using infinitesimal jackknife method (1000 iterations). Corrects for optimism in subgroup selection.
³ Identified subgroup: {er <= 0}
Note: Med = Median survival time (months). RMST_d = Restricted mean survival time difference. Subgroup identified in 87.4% of bootstrap samples.

6.4 Kaplan-Meier by Identified Subgroups

Show code

 km_result <- plot_sg_weighted_km(
   fs.est = fs,
   outcome.name = "time_months",
   event.name = "status",
   treat.name = "hormon",
   show.logrank = FALSE,
   conf.int = TRUE,
   by.risk = 12,
   show.cox = FALSE, show.cox.bc = TRUE,
   fs_bc = fs_bc,
   hr_bc_position = "topright"
 )

Kaplan-Meier survival curves by identified subgroup

Note: Identified subgroup: {er <= 0}. HR(bc) = bootstrap bias-corrected hazard ratio. Medians [95% CI] for arms are un-adjusted.

6.4.1 Event Count Summary

Low event counts can lead to unstable HR estimates. This summary helps identify potential issues:

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# note that default required minimum events is 12 for subgroup candidate
# Here we evaluate frequency of subgroup candidates in bootstrap samples less than 15
event_summary <- summarize_bootstrap_events(fs_bc, threshold = 15)


=== Bootstrap Event Count Summary ===
Total bootstrap iterations: 1000
Event threshold: <15 events

ORIGINAL Subgroup H on BOOTSTRAP samples:
  Control arm <15 events: 0 (0.0%)
  Treatment arm <15 events: 0 (0.0%)
  Either arm <15 events: 0 (0.0%)

ORIGINAL Subgroup Hc on BOOTSTRAP samples:
  Control arm <15 events: 0 (0.0%)
  Treatment arm <15 events: 0 (0.0%)
  Either arm <15 events: 0 (0.0%)

NEW Subgroups found: 874 (87.4%)

NEW Subgroup H* on ORIGINAL data:
  Control arm <15 events: 23 (2.6% of successful)
  Treatment arm <15 events: 113 (12.9% of successful)
  Either arm <15 events: 128 (14.6% of successful)

NEW Subgroup Hc* on ORIGINAL data:
  Control arm <15 events: 0 (0.0% of successful)
  Treatment arm <15 events: 0 (0.0% of successful)
  Either arm <15 events: 0 (0.0% of successful)

6.4.2 Bootstrap Diagnostics

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# Quality metrics
summaries$diagnostics_table_gt

Category	Metric	Value
Bootstrap Diagnostics Summary
Analysis of 1000 bootstrap iterations
Success Rate	Total iterations	1000
	Successful	874 (87.4%)
	Failed	126 (12.6%)
	Success rating	Good
Subgroup H (Questionable)	Observed HR	1.951
	Bias-corrected HR	1.528
	Bootstrap CV (%)	99.3%
	N estimates	874
Subgroup Hc (Recommend)	Observed HR	0.615
	Bias-corrected HR	0.643
	Bootstrap CV (%)	48.7%
	N estimates	874

6.4.3 Subgroup Agreement

How consistently does bootstrap identify the same subgroup?

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# Agreement with original analysis
if (!is.null(summaries$subgroup_summary$original_agreement)) {
  summaries$subgroup_summary$original_agreement
}

                            Metric       Value
                            <char>      <char>
1:      Total bootstrap iterations        1000
2:           Successful iterations         874
3: Failed iterations (no subgroup)         126
4:                                            
5:    Original subgroup definition   {er <= 0}
6:       Exact match with original 108 (12.4%)
7:         Different from original 766 (87.6%)
8:   Partial match (shared factor) 121 (13.8%)

Show code

# Factor presence across bootstrap iterations
if (!is.null(summaries$subgroup_summary$factor_presence)) {
  summaries$subgroup_summary$factor_presence
}

  Rank Factor Count   Percent
6    1    pgr   427 48.855835
2    2     er   358 40.961098
7    3   size   293 33.524027
1    4    age   281 32.151030
5    5  nodes   110 12.585812
3    6 grade3   102 11.670481
4    7   meno    55  6.292906

6.4.4 Bootstrap Distributions

Show code

if (!is.null(summaries$plots)) {
  summaries$plots$H_distribution + summaries$plots$Hc_distribution
}

7 Cross-Validation

Cross-validation assesses the stability of the ForestSearch algorithm. Two approaches are available:

7.1 K-Fold Cross-Validation

Show code

# 10-fold CV with multiple iterations
# Use Ksims >= 50 for production
Ksims <- 30

t0 <- proc.time()

fs_kfold <- forestsearch_tenfold(
  fs.est = fs,
  sims = Ksims,
  Kfolds = 10,
  details = FALSE,
  parallel_args = list(
    plan = "multisession",
    workers = n_cores,
    show_message = FALSE
  )
)

plan("sequential")
timings$kfold <- (proc.time() - t0)["elapsed"]


metrics_tables <- cv_metrics_tables(fs_kfold)

metrics_tables

Metric	Description	Value (%)
Cross-Validation Metrics
Subgroup: Identified Subgroup
Agreement
Sensitivity (H)	Agreement rate for subgroup H	53.7
Sensitivity (Hc)	Agreement rate for complement Hc	98.8
PPV (H)	Positive predictive value for H	82.6
PPV (Hc)	Positive predictive value for Hc	94.0
Subgroup Finding
Any Found	Any subgroup identified	65.0
Exact Match	Exact match on all factors	50.0
At Least 1	At least one factor matches	50.0
Cov1 Any	First covariate found (any cut)	55.0
Cov2 Any	Second covariate found (any cut)	NA
Cov1 & Cov2	Both covariates found	0.0
Cov1 Exact	First covariate exact match	50.0
Cov2 Exact	Second covariate exact match	NA
Based on 30 simulation(s) with 10-fold CV. Values are medians shown as percentages.

7.2 Out-of-Bag (N-Fold) Cross-Validation

N-fold CV (leave-one-out):

Show code

t0 <- proc.time()

fs_OOB <- forestsearch_Kfold(
  fs.est = fs,
  details = FALSE,
  Kfolds = nrow(df.analysis),  # N-fold = leave-one-out
  parallel_args = list(
    plan = "multisession",
    workers = n_cores,
    show_message = TRUE
  )
)

plan("sequential")
timings$oob <- (proc.time() - t0)["elapsed"]

# Summarize OOB results

cv_out <- forestsearch_KfoldOut(
  res = fs_OOB,
  details = FALSE,
  outall = TRUE
)

tables <- cv_summary_tables(cv_out)

tables$combined_table

Analysis	Subgroup	n	n1	m1	m0	RMST	Hazard ratio
Cross-Validation Summary
ITT and Subgroup Estimates: Full Analysis (FA) vs K-fold (Kf)
Overall	ITT	686 (100.0%)	246 (35.9%)	66.3	50.2	7.8	0.69 (0.54, 0.89)
FA_0	Not recommend	82 (12.0%)	26 (31.7%)	22.9	43.7	-14	1.95 (1.04, 3.67)
KfA_0	Not recommend	68 (9.9%)	16 (23.5%)	38.9	42.9	2.9	0.85 (0.37, 1.97)
FA_1	Recommend	604 (88.0%)	220 (36.4%)	66.7	52.6	9.3	0.61 (0.47, 0.80)
KfA_1	Recommend	618 (90.1%)	230 (37.2%)	66.3	55	7	0.70 (0.54, 0.90)
FA = Full Analysis (original data), Kf = K-fold CV estimate

Show code

tables$metrics_table

Metric	Value (%)
Cross-Validation Metrics
Agreement and subgroup finding rates (%)
Agreement
Sensitivity (H)	82.9
Sensitivity (Hc)	100.0
PPV (H)	100.0
PPV (Hc)	97.7
Finding
Any Found	97.8
Exact Match	97.8
At Least 1	97.8
Cov1 Any	97.8
Cov2 Any	NaN
Cov1 & Cov2	0.0
Cov1 Exact	97.8
Cov2 Exact	NaN

8 Results Visualization

8.1 Forest Plot

The forest plot summarizes treatment effects across the ITT population, reference subgroups, and identified subgroups with cross-validation metrics.

Show code

# Define reference subgroups for comparison
subgroups <- list(
  age_gt65 = list(
    subset_expr = "age > 65",
    name = "Age > 65",
    type = "reference"
  ),
  age_le65 = list(
    subset_expr = "age <= 65",
    name = "Age ≤ 65",
    type = "reference"
  ),
  pgr_positive = list(
    subset_expr = "pgr > 0",
    name = "PgR > 0",
    type = "reference"
  ),
  pgr_negative = list(
    subset_expr = "pgr <= 0",
    name = "PgR ≤ 0",
    type = "reference"
  )
)


my_theme <- create_forest_theme(base_size = 24, 
footnote_fontsize = 17, cv_fontsize = 22)


# Create forest plot
# Include fs_kfold and fs_OOB if available for CV metrics
result <- plot_subgroup_results_forestplot(
  fs_results = list(
    fs.est = fs,
    fs_bc = fs_bc,
    fs_OOB = NULL,
    fs_kfold = fs_kfold
  ),
  df_analysis = df.analysis,
  subgroup_list = subgroups,
  outcome.name = outcome.name,
  event.name = event.name,
  treat.name = treat.name,
  E.name = "Hormonal",
  C.name = "Chemo",
  ci_column_spaces = 25,
  xlog = TRUE,
  theme = my_theme
)


# Option 2: Custom sizing
render_forestplot(result)

Subgroup forest plot including identified subgroups

8.1.1 KM Difference plots: ITT and subgroups

The solid black line denotes the ITT Kaplan-Meier treatment difference estimates along with 95%95% CIs (the grey shaded region). K-M differences corresponding to subgroups are displayed.

Show code

# Add additional subgroups along with ITT and identified subgroups
ref_sgs <- list(
age_young = list(subset_expr = "age < 65", color = "brown"),
age_old = list(subset_expr = "age >= 65", color = "orange")
)

plot_km_band_forestsearch(
 df = df.analysis,
   fs.est = fs,
 ref_subgroups = ref_sgs,
 outcome.name = outcome.name,
   event.name = event.name,
   treat.name = treat.name,
 draws_band = 1000
)

Show code

# # Example with more subgroups
# ref_sgs <- list(
# pgr_positive = list(subset_expr = "pgr > 0", color ="green"),
# pgr_negative = list(subset_expr = "pgr <= 0", color = "purple"),
# age_young = list(subset_expr = "age < 65", color = "brown"),
# age_old = list(subset_expr = "age >= 65", color = "orange")
# )

9 Summary and Interpretation

9.1 Key Findings

Show code

# Extract key results
cat("=" %>% rep(60) %>% paste(collapse = ""), "\n")

============================================================

Show code

cat("FORESTSEARCH ANALYSIS SUMMARY\n")

FORESTSEARCH ANALYSIS SUMMARY

Show code

cat("=" %>% rep(60) %>% paste(collapse = ""), "\n\n")

============================================================

Show code

cat("Dataset: GBSG (N =", nrow(df.analysis), ")\n")

Dataset: GBSG (N = 686 )

Show code

cat("Outcome: Recurrence-free survival\n\n")

Outcome: Recurrence-free survival

Show code

cat("ITT Analysis:\n")

ITT Analysis:

Show code

cat("  HR (95% CI): 0.69 (0.54, 0.89)\n\n")

  HR (95% CI): 0.69 (0.54, 0.89)

Show code

cat("Identified Subgroup (H):\n")

Identified Subgroup (H):

Show code

cat("  Definition:", paste(fs$sg.harm, collapse = " & "), "\n")

  Definition: {er <= 0}

Show code

cat("  Size:", sum(fs$df.est$treat.recommend == 0), 
    sprintf("(%.1f%%)\n", 100 * mean(fs$df.est$treat.recommend == 0)))

  Size: 82 (12.0%)

Show code

cat("  Unadjusted HR:", sprintf("%.2f", exp(fs$grp.consistency$out_sg$result$hr[1])), "\n")

  Unadjusted HR: 7.04

Show code

cat("\nComplement Subgroup (Hc):\n")


Complement Subgroup (Hc):

Show code

cat("  Size:", sum(fs$df.est$treat.recommend == 1),
    sprintf("(%.1f%%)\n", 100 * mean(fs$df.est$treat.recommend == 1)))

  Size: 604 (88.0%)

9.2 Clinical Interpretation

The ForestSearch analysis identifies estrogen receptor-negative (ER ≤ 0) patients as a subgroup with potential lack of benefit from hormonal therapy.

Biological plausibility: Tamoxifen is a selective estrogen receptor modulator. Its efficacy depends on ER expression. The finding that ER-negative patients may not benefit is consistent with:

Mechanistic understanding of tamoxifen action
Meta-analyses showing no tamoxifen benefit in ER-negative breast cancer
Clinical guidelines recommending tamoxifen primarily for ER-positive tumors

Caveats:

This is an exploratory analysis requiring independent validation
The bias-corrected estimates have wider confidence intervals
Cross-validation metrics should be evaluated for algorithm stability

9.3 Computational Timing

Show code

timings$total <- (proc.time() - t_vignette_start)["elapsed"]

timing_df <- data.frame(
  Analysis = c("GRF", "ForestSearch", "Bootstrap", "Kfold","OOB","Total"),
  Seconds = c(
    timings$grf,
    timings$forestsearch,
    timings$bootstrap,
    timings$kfold,
    timings$oob,
    timings$total
  )
)
timing_df$Minutes <- timing_df$Seconds / 60

gt(timing_df) |>
  tab_header(title = "Computational Timing") |>
  fmt_number(columns = c(Seconds, Minutes), decimals = 1) |>
  cols_label(
    Analysis = "Component",
    Seconds = "Time (sec)",
    Minutes = "Time (min)"
  )

Component	Time (sec)	Time (min)
Computational Timing
GRF	0.2	0.0
ForestSearch	6.8	0.1
Bootstrap	559.0	9.3
Kfold	119.2	2.0
OOB	343.3	5.7
Total	1,030.9	17.2

10 References

León LF, Jemielita T, Guo Z, Marceau West R, Anderson KM (2024). “Exploratory subgroup identification in the heterogeneous Cox model: A relatively simple procedure.” Statistics in Medicine. DOI: 10.1002/sim.10163

11 Session Information

Show code

sessionInfo()

R version 4.5.1 (2025-06-13)
Platform: aarch64-apple-darwin20
Running under: macOS Tahoe 26.2

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/Los_Angeles
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] weightedsurv_0.1.0      patchwork_1.3.2         doRNG_1.8.6.2          
 [4] rngtools_1.5.2          doFuture_1.2.0          future_1.69.0          
 [7] foreach_1.5.2           policytree_1.2.3        grf_2.5.0              
[10] gt_1.3.0                ggplot2_4.0.1           data.table_1.18.0      
[13] survival_3.8-6          forestsearch_0.0.0.9000

loaded via a namespace (and not attached):
 [1] gtable_0.3.6         shape_1.4.6.1        xfun_0.53           
 [4] htmlwidgets_1.6.4    visNetwork_2.1.4     lattice_0.22-7      
 [7] vctrs_0.6.5          tools_4.5.1          generics_0.1.4      
[10] parallel_4.5.1       tibble_3.3.0         pkgconfig_2.0.3     
[13] Matrix_1.7-3         forestploter_1.1.3   RColorBrewer_1.1-3  
[16] S7_0.2.0             lifecycle_1.0.4      compiler_4.5.1      
[19] farver_2.1.2         stringr_1.6.0        codetools_0.2-20    
[22] litedown_0.7         htmltools_0.5.8.1    sass_0.4.10         
[25] yaml_2.3.10          glmnet_4.1-10        pillar_1.11.1       
[28] iterators_1.0.14     parallelly_1.46.1    commonmark_2.0.0    
[31] tidyselect_1.2.1     digest_0.6.37        stringi_1.8.7       
[34] dplyr_1.1.4          listenv_0.9.1        labeling_0.4.3      
[37] splines_4.5.1        fastmap_1.2.0        grid_4.5.1          
[40] cli_3.6.5            magrittr_2.0.4       DiagrammeR_1.0.11   
[43] base64enc_0.1-3      randomForest_4.7-1.2 future.apply_1.20.1 
[46] withr_3.0.2          scales_1.4.0         rmarkdown_2.30      
[49] globals_0.18.0       gridExtra_2.3        progressr_0.18.0    
[52] evaluate_1.0.5       knitr_1.51           markdown_2.0        
[55] rlang_1.1.6          Rcpp_1.1.0           glue_1.8.0          
[58] xml2_1.4.0           rstudioapi_0.17.1    jsonlite_2.0.0      
[61] R6_2.6.1             fs_1.6.6